Question

video lesson 5.5 example 6 - finding a probability using combinations

1. the art teacher has selected 13 projects, including one of yours and one of your friend’s, to use in a display case in the hallway. the projects are placed at random. there is room for 2 projects in the middle row of the case. what is the probability that your project and your friend’s project are the two placed in the middle row?

Explanation:

Step1: Calculate total combinations

We use the combination formula \( C(n, k) = \frac{n!}{k!(n - k)!} \), where \( n = 13 \) (total projects) and \( k = 2 \) (projects in the middle row). So, \( C(13, 2) = \frac{13!}{2!(13 - 2)!} = \frac{13\times12}{2\times1} = 78 \).

Step2: Calculate favorable combinations

There's only 1 favorable combination (your project and your friend’s project).

Step3: Find the probability

Probability is favorable combinations divided by total combinations, so \( \frac{1}{78} \).

Answer:

\(\frac{1}{78}\)